1. Field of the Invention
The invention concerns an optical device for the processing of an optical wave, its method of fabrication and a frequency doubler.
More particularly, it concerns a device and a method enabling major optical non-linear effects to be obtained in waveguides made of ferroelectric materials.
2. Description of the
It is well known that the electrical polarization induced in a medium by an electromagnetic wave can be written out as follows: EQU P=d.sup.(1) E+d.sup.(2) EE+. . .
where E is the electric magnetic field associated with the electromagnetic wave.
In this expression, the first term is responsible for the linear properties of the material and the following terms are responsible for the non-linear properties which can give rise to phenomena of frequency doubling, tripling, addition etc.
The even-order terms exist only in media having no center of symmetry.
For such non-linear interactions to be effective, it is generally necessary to ascertain that there is a condition called a phase-matching condition. For, at every point, the non-linear polarization will radiate an electromagnetic field having the same frequency but with a phase that will be determined by the sum of the phases of the generating fields at this point. On the other hand, the phase of the radiated field will naturally behave differently and, in particular, will depend on the refractive index of the medium at the harmonic frequency.
In fact, another way to formulate this condition is to assume that two conditions have to be considered for such non-linear interactions to be effective:
1) Conservation of energy PA1 2) Conservation of the moments (wave vectors in this case) PA1 k (2w)=2 k(w) PA1 2 (2.pi.n(w)) // F=n(2w) 2.pi./.lambda.(2w) PA1 .lambda.(w) being the wavelength of the fundamental PA1 .lambda.(2w) being the harmonic wavelength. PA1 n.sub.o (w) is the index of the medium for the wavelength of the fundamental PA1 n.sub.e (2w) is the index of the medium for the harmonic PA1 giving n.sub.e (2w)=n.sub.o (w) PA1 Article by N. BLOEMBERGEN et al in Applied Physics Lettters, 17, 483, 1970; PA1 Article by B. JASKORZYNSKA et al in SPIE volume 651, Innsbruck, 1986; PA1 Article by T. TANIUCHI et al in SPIE, volume 864, Cannes, 1987. PA1 a two-dimensional optical guide, implanted in the surface of the substrate and oriented along a first direction; PA1 doping zones distributed along the optical guide, each doping zone having a length, along the first direction, which is an odd multiple of the length of coherence (Lc), and the distribution pitch of doping zones having a value that is an even multiple of the length of coherence, the doping zones giving rise to a reversal of the polarization of the optical wave with respect to the the polarization in the zones included between the doping zones. PA1 a) the making, on one face of a transparent ferroelectric substrate, of doping zones distributed along a first direction with a pitch equal to an even multiple of the length of coherence (Lc), each zone having a length equal to an odd multiple of the length of coherence (Lc), the doping being such that it reverses the polarization of the wave with respect to that in the non-doped zones; PA1 b) the making of an optical guide in the first direction.
For simplicity's sake, let us consider the case of the generation of a second harmonic. In this case, we have: EQU P(2w) proportionate to d.sup.(2) E(w)E(w)
and hence:
It is this latter condition that is called "phase matching".
This condition may be achieved, in practice, by using for example the birefringency of the material. In this case, the harmonic wave (2w) and the fundamental wave (w) can be polarized according to the different inherent directions of the crystal being used. For example, if the harmonic wave is extraordinarily polarized and if the two fundamental waves coming into the interaction are ordinarily polarised, the following has to be ascertained: EQU 2(2.pi.n.sub.o (w))/.lambda.(w)=n.sub.e (2w)2.pi./.lambda.(2w)
where
This condition can be achieved in certain materials either by using temperature effects or by changing the angle of propagation with respect to the optical axis n.sub.e =f (angle). The angle considered is the angle between the direction of propagation and the optical axis of the material considered.
Other techniques may be used to set up the phase matching, such as those described in the following documents:
For example, the presence of a diffraction grating within the material can lead to a cancellation of the mismatching between K (2w) and 2K (w) if the period of the grating is accurately chosen.
We should have:
K(2w) - 2 k(w)=mK (grating) where m is an integer and K is the wave vector associated with the grating (k-2.pi./period).
In such an interaction, the grating may be created on the basis of either the linear properties of the material or its non-linear properties. In the latter case, it is advantageous (more efficient) to create a change in the sign of the non-linear coefficient concerned.
This technique is particularly valuable with materials having non-linear coefficients that cannot be used with standard phase matching methods. This, for example, is the case with the non-linear coefficients X33 of LiNbO.sub.3 and LiTaO.sub.3 which bring into play fundamental and harmonic waves polarized along the optical axis of these materials (extraordinary polarization).
If we consider the case of LiNbO.sub.3 with X33, demonstrations have been given by periodically reversing the ferroelectric polarization (and hence the sign of X33) during the growth of the crystal (as described in the article by D. FENG in Applied Physics Letter, 37, 607, 1980).
The goal of the invention is to propose means that enable periodical reversals of the non-linear coefficient of an optical guide.